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Structures revealed in the neutron-proton mass spectrum in the deuteron break-up reaction
Volume 128B, number 5
PHYSICS LETTERS
1 September 1983
STRUCTURES REVEALED IN THE NEUTRON-PROTON MASS SPECTRUM IN THE DEUTERON BREAK-UP REACTION T. SIEMIARCZUK, J. STEPANIAK and P. ZIELII(ISKI High Energy Physics Laboratory, Institute for Nuclear Research, Ho~a 69, 00-681 Warsaw,Poland Received 22 April 1982 Revised manuscript received 29 March 1983
A sample of "non-spectator" events in the dp ~ (pn) p break-up reaction at 3.3 GeV/c deuteron momentum is studied using films from 1 m hydrogen bubble chamber. The effective mass distribution of two nucleons from the deuteron breakup exhibits enhancements near the sum of neutron and proton masses and at Mpn = 2020 and 2130 MeV.
In recent papers (for review see ref. [1] and references contained therein) the possible existence of several candidates for I = 0 and ! = 1 dibaryon resonances has been reported. Some observations correspond to the positions of dips in the elastic CLL spin-correlation data [2], others are obtained from cross section differences between parallel and antiparallel transverse and longitudinal total cross sections [3]. An evidence comes also from the phase-shift [4] and dispersion relation [5] analysis and from the observation of energy dependence in proton polarization in the 7d ~ pn reaction [6,7]. To our knowledge, apart from the total cross section measurements, the only attempts to look for the non-strange dibaryon resonances by studying the two-nucleon effective mass distribution were concerned with xenon [8,9], carbon [10,11] and deuterium [12] nucleus fragmentation by using the bubble chamber technique. In xenon and carbon studies the analysed interval of two-proton excitation energy Q = Mpp - 2rap was rather small ( 0 - 1 0 0 MeV) due to the low energy of proton fragments taken for analysis. The range of stopping protons was measured and the obtained resolution of two-proton effective mass was about few MeV. Only one statistically significant signal at Q -~ 0 with a width of about 5 MeV has been observed [8] and confirmed lately [10,11,13]. The aim of the present work was to perform a similar study with a good effective mass resolution in wider range of two-nucleon excitation energy. We are 0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
concerned here only with a neutron-proton system. The observation in this experiment of a dibaryon candidate in the pp system with a mass of 2170 MeV (P ~-- 50 MeV) has been already reported [12]. The experiment was performed by exposing lm hydrogen bubble chamber to a 3.3 GeV/c deuteron beam. The details of the experiment were published elsewhere [ 14]. A sample of 18593 deuteron break-up dp ~ pnp events has been collected. The break-up events can be distinctly separated into two processes: the charge exchange reaction dp ~ (pp)n corresponding to the configuration when the neutron momentum is higher than that of any proton in the deuteron rest system, and the remaining charge retention events proceeding without charge exchange between the projectile and the target: dp ~ (pn)p [14]. The following advantages of using the deuteron beam should be pointed out [15]: (i) No mixing takes place between elastic and break-up channels; this mixing is common for the deuterium target experiments where about 90% of elastic pd ~ pd events yield a one-constraint fit to the deuteron break-up channel. In our beam-target configuration the curvature of the fast outgoing proton is about twice as large as that of the deuteron from the elastic event providing clean separation between elastic and break-up events. (ii) There is also very distinct separation between the dp ppn and dp ~ ppn + neutrals channels, since the missing mass resolution is much less than the mass of 367
Volume 128B, number 5
PHYSICSLETTERS
1 September 1983
J Jt
41
~r o
w tO
I IL~l 10
i, 50
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I, 100
I
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Opn ( MeV ) Fig. 1. The resolution in excitation energy of the proton-neutron system as a function of Qpn.
Ir° meson. (iii) No losses occur in proton spectators, whereas in case of the deuterium target, the protons with momentum Ps < 80 MeV/c are invisible in the bubble chamber. In the following we analyse the charge retention channel dp ~ (rip)p (15333 events in total with a normalization of 2.01/ab per event) excluding from the break-up sample the charge exchange channel dp (pp)n (3260 events) reported previously [12]. Fig. 1 shows the resolution in excitation energy of np system as a function of Qpn" The resolution is about 2 MeV near the threshold, increases to about 10 MeV around Qpn -~ 100 MeV and then levels approximately off. Note, that the excitation energy resolution in the deuterium bubble chamber experiments is about 4 0 - 5 0 MeV. The full line shows the width of the o(Qpn ) distribution as a function of Qpn" It is well known that for the nucleons so loosely bound as in the deuteron the probability of exciting the whole neutron-proton system from the deuteron is rather small because of the large contribution of the single scattering. If we look on the momentum distribution of the slowest nucleon (we call it spectator) in the deuteron rest frame, its behaviour is very much spectator-like [16,17] up to the momentum of about 250-300 MeV/c, whereas for, say, Ps > 350 MeV/c a substantial excess of events is observed being about seven times higher than the predictions based on the conventional H01then wave function and more 368
than twice as large as the tail prredicted by the Reid soft core wave function (having one of the "thickest" tails) with D wave included. If we make a cut on Ps and plot events with Ps > 350 MeV/c, then three enhancements in Qpn are to be found: at threshold, at about 140 MeV and at 240 MeV, as is shown in fig. 2. The first one at Qpn ~-"0 is akeady known (see e.g. refs. [18,19]) and is usually ascribed to the FSI in the 1 So state of the neutronproton system. Three possible background processes capable of simulating the observed enhancements were considered: (i) Since one might expect some contribution of the single scattering mechanism, the peripheral phase space for proton elementary reaction on bound nucleon was generated by the modified FOWL programme and combined with the spectator nucleon generated according to the following procedure: (a) The spectator nucleon was assumed to be on the mass shell, whereas the mass of the "active" nucleon was calculated from the formula: ma = ([md _ (m 2 + p2)1/212 _ p2~1/2 , where rod, m and Ps are the mass of the deuteron, the nucleon mass and the spectator nucleon momentum generated according to the Reid soft core wave function for Ps > 0.35 GeV/c with D wave contribution taken into account. (b) The momentum of the "active" nucleon was assumed to be opposite to that of
Volume 128B, number 5
PHYSICS LETTERS
1 September 1983
40
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30
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Op°(MeV) Fig. 2. The excitation energy distribution for the "non-spectator" (ps > 350 MeV/c) sample. The dashed and dotted lines represent the background originated from single and double scattering, respectively. The solid lines refer to the dp ~ pnp three-body phase space alone and together with the two Breit-Wigner distributions.
the spectator one. (c) The angle of emission of the spectator in the deuteron rest system was generated from the isotropic distribution and it was checked for each event whether the generated momentum and the angle of emission are allowed kinematically. (d) The dependence of the slope of four-momentum transfer distribution on the cms energy of the projectile and the moving off shell nucleon from the deuteron was taken into account in the pheripheral phase space calculations [16,20]. The dashed line in fig. 2 shows the result of calculations. The curve is normalized to the half of the events to account for the maximum possible contribution of single scattering. (ii) Likewise we haveexamined the background due to the double scattering effects. The Glauber type calculations [21] yield its maximum contribution of about 3% to all dp -+ (pn)p break-up events, whereas
the sample studied amounts to about 6% of the total number of events. The double scattering background was calculated by using our modified version of FOWL programme and both scatterings were treated in a similar fashion as the first one in the single scattering calculations, with the only difference that in the second collision the nucleon hit by the projectile was already on the mass shell. The Qpn background originated from the double scattering, shown in fig. 2 by dotted line, is quite flat in the interval from 100 to 200 MeV and drops slowly for higher Qpn" Note, that in the impulse approximation and in the double scattering calculations we neglect the FSI in the 3 S1 state [ 16] leading to the formation of deuteron which should certainly reduce the number of events with small Qpn by changing the assignment of the event from one of deuteron break-up back to one of elastic scattering. It is seen from fig. 2 that neither 369
Volume 128B, number 5
PHYSICS LETTERS
the single scattering curve nor the double scattering one nor their sum are able to reproduce the data or be responsible for the observed enhancements. (iii) The three body dp -->pnp phase space was generated and is shown in fig. 2 by solid line. Apart from the Qpn intervals where the enhancements are present, it resembles quite reasonably the shape of the experimental distribution. Leaving aside the threshold enhancement which requires special FSI calculation, we fitted two Breit-Wigner distributions and this background to the data in the Qpn interval from 55 to 275 MeV. The upper cut o f the interval in which the fit was performed is due to some excess of events present in the vicinity o f Qpn ~ 400 MeV. The result of the fit and the background alone are shown in fig. 2 b y solid line. With exception o f the region of the threshold signal, the three-body phase space background and two Breit-Wigner distributions agree fairly well with the data. The small accumulation o f events at about 400 MeV is close to the mass o f the Argonne dibaryon candidate [22] and might be its " p r o t o n neutron" counterpart, but statistics is very limited here. The masses, the widths and the cross sections obtained from the fit are: Q1 = 1 3 5 + 1 0 M e V FI
(M 1 = 2 0 2 0 - + 1 0 M e V ) ,
=45-+20MeV,
o(/1//1) = 200 + 20 p b , Q2 = 2 4 0 + 1 0 M e V
(M 2 = 2 1 3 0 + 1 0 M e V ) ,
F 2 = 20 + l 0 MeV, o(/I//2) = 85 -+ 15 p b , The angular distributions o f nucleons from the (np) excited system in the (np) rest frame with respect to the incoming proton direction were examined for the overall sample in two standard deviation intervals around the masses of the enhancements. The angular distributions exhibit f o r w a r d - b a c k w a r d symmetry, the isotropic component is present in both distributions and the fractions of events distributed isotropicaUy are consistent with the cross sections obtained from the fit for 2020 and 2130 MeV signals. The masses of the observed enhancements fit surprisingly well into the simple scheme developed by MacGregor [23]. He found that the masses o f already
370
1 September 1983
reported 1 D2 ' 3 F3 and 1G 4 [2] dibaryon resonances in the pp system follow a straight line when plotted against I(l + 1). If one assumes, b y analogy to the nuclear physics rotational band, that this is due to the difference in rotational energy, the extrapolation to l = 0 yields a mass o f 2020 MeV, exactly the mass we observe. The second enhancement at 2130 agrees with l = 2 state with the predicted mass o f 2140 MeV. In conclusion we wish to emphasize that there already exist data obtained by working with an incident deuteron beam at higher energies (e.g. at 11.6 [24] and 24 GeV/c [25]) and it would be o f great interest to perform a similar analysis for the "non-spectator" sample. Also the deuterium bubble chamber experiments could yield, with somewhat worse resolution, valuable information about possible dibaryon states.
References [1] A. Yokosawa, ANL report m. ANL-HEP-CP-80-01 (1980), to be published in: Proc. Intern. Meeting on Two-nucleon systems and dibaxyon resonances (Hiroshima, 1979). [2] I.P. Auer et al., Phys. Rev. Lett. 41 (1978) 1436. [ 3] A. Yokosawa, ANL report rtr. ANL-HEP-CP-78-52 (1978). [4] N. Hoshizaki, Prog. Theor. Phys. 60 (1978) 1796. [5] W. Grein and P. KroU, Nucl. Phys. B137 (1978) 173. [6] H. Ikeda et al., Phys. Rev. Lett. 42 (1979) 1321. [7] T. Kamae et al., Phys. Rev. Lett. 38 (1977) 471. [8] T. Siemiarczuk and P. Zielifiski, Phys. Lett. 24B (1967) 675. [9] B. Balcer et al., Acta Phys. Pol. 33 (1968) 619. [10] S. Azimov et al., Yad. Fiz. 19 (1974) 317. [11 ] N. Angelov et al., JINR report P1-80-55 (1980). [12] B.S. Aladashvili et al., Nuel. Phys. A274 (1976) 486. [ 13 ] B.S. Aladashvili et al., J. Phys. (NY) G3 (1977) 1225. [14] B.S. Aladashvili et al., Nucl. Instrum. Methods 129 (1975) 109. [15] R. Harris, Ph.D. Thesis, VTL-PUB-22, University of Washington (1975). [16] B.S. Aladashvili et al., J. Phys. (NY) G3 (1977) 7. [17] G. Alberi et al., Nucl. Phys. B108 (1976) 327. [18] T.R. Witten et al., Nucl. Phys. B108 (1976) 327. [191 T. Ericson, Adv. Phys. 9 (1960) 425. [20] E. Byckling and K. Kajantie, Nuel. Phys. B9 (1969) 568. [21] B.S. Aladashvili et al., Nucl. Phys. B92 (1975) 189. [221 A. Yokosawa, Phys. Rep. 64 (1980) 49. [23] M.H. MacGregor, Phys. Rev. Lett. 42 (1979) 1724. [24] D. Hochman et al., Nucl. Phys. B68 (1974) 301. [25] J.W. Cooper et al., Nucl. Phys. B79 (1974) 259.
PHYSICS LETTERS
1 September 1983
STRUCTURES REVEALED IN THE NEUTRON-PROTON MASS SPECTRUM IN THE DEUTERON BREAK-UP REACTION T. SIEMIARCZUK, J. STEPANIAK and P. ZIELII(ISKI High Energy Physics Laboratory, Institute for Nuclear Research, Ho~a 69, 00-681 Warsaw,Poland Received 22 April 1982 Revised manuscript received 29 March 1983
A sample of "non-spectator" events in the dp ~ (pn) p break-up reaction at 3.3 GeV/c deuteron momentum is studied using films from 1 m hydrogen bubble chamber. The effective mass distribution of two nucleons from the deuteron breakup exhibits enhancements near the sum of neutron and proton masses and at Mpn = 2020 and 2130 MeV.
In recent papers (for review see ref. [1] and references contained therein) the possible existence of several candidates for I = 0 and ! = 1 dibaryon resonances has been reported. Some observations correspond to the positions of dips in the elastic CLL spin-correlation data [2], others are obtained from cross section differences between parallel and antiparallel transverse and longitudinal total cross sections [3]. An evidence comes also from the phase-shift [4] and dispersion relation [5] analysis and from the observation of energy dependence in proton polarization in the 7d ~ pn reaction [6,7]. To our knowledge, apart from the total cross section measurements, the only attempts to look for the non-strange dibaryon resonances by studying the two-nucleon effective mass distribution were concerned with xenon [8,9], carbon [10,11] and deuterium [12] nucleus fragmentation by using the bubble chamber technique. In xenon and carbon studies the analysed interval of two-proton excitation energy Q = Mpp - 2rap was rather small ( 0 - 1 0 0 MeV) due to the low energy of proton fragments taken for analysis. The range of stopping protons was measured and the obtained resolution of two-proton effective mass was about few MeV. Only one statistically significant signal at Q -~ 0 with a width of about 5 MeV has been observed [8] and confirmed lately [10,11,13]. The aim of the present work was to perform a similar study with a good effective mass resolution in wider range of two-nucleon excitation energy. We are 0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
concerned here only with a neutron-proton system. The observation in this experiment of a dibaryon candidate in the pp system with a mass of 2170 MeV (P ~-- 50 MeV) has been already reported [12]. The experiment was performed by exposing lm hydrogen bubble chamber to a 3.3 GeV/c deuteron beam. The details of the experiment were published elsewhere [ 14]. A sample of 18593 deuteron break-up dp ~ pnp events has been collected. The break-up events can be distinctly separated into two processes: the charge exchange reaction dp ~ (pp)n corresponding to the configuration when the neutron momentum is higher than that of any proton in the deuteron rest system, and the remaining charge retention events proceeding without charge exchange between the projectile and the target: dp ~ (pn)p [14]. The following advantages of using the deuteron beam should be pointed out [15]: (i) No mixing takes place between elastic and break-up channels; this mixing is common for the deuterium target experiments where about 90% of elastic pd ~ pd events yield a one-constraint fit to the deuteron break-up channel. In our beam-target configuration the curvature of the fast outgoing proton is about twice as large as that of the deuteron from the elastic event providing clean separation between elastic and break-up events. (ii) There is also very distinct separation between the dp ppn and dp ~ ppn + neutrals channels, since the missing mass resolution is much less than the mass of 367
Volume 128B, number 5
PHYSICSLETTERS
1 September 1983
J Jt
41
~r o
w tO
I IL~l 10
i, 50
II
I, 100
I
i
I
I I 150
i
i
I
[ 200
i
i
I
I
i
250
,
,
t
~
t
300
L
J
,
,
I
,
,
,
350
Opn ( MeV ) Fig. 1. The resolution in excitation energy of the proton-neutron system as a function of Qpn.
Ir° meson. (iii) No losses occur in proton spectators, whereas in case of the deuterium target, the protons with momentum Ps < 80 MeV/c are invisible in the bubble chamber. In the following we analyse the charge retention channel dp ~ (rip)p (15333 events in total with a normalization of 2.01/ab per event) excluding from the break-up sample the charge exchange channel dp (pp)n (3260 events) reported previously [12]. Fig. 1 shows the resolution in excitation energy of np system as a function of Qpn" The resolution is about 2 MeV near the threshold, increases to about 10 MeV around Qpn -~ 100 MeV and then levels approximately off. Note, that the excitation energy resolution in the deuterium bubble chamber experiments is about 4 0 - 5 0 MeV. The full line shows the width of the o(Qpn ) distribution as a function of Qpn" It is well known that for the nucleons so loosely bound as in the deuteron the probability of exciting the whole neutron-proton system from the deuteron is rather small because of the large contribution of the single scattering. If we look on the momentum distribution of the slowest nucleon (we call it spectator) in the deuteron rest frame, its behaviour is very much spectator-like [16,17] up to the momentum of about 250-300 MeV/c, whereas for, say, Ps > 350 MeV/c a substantial excess of events is observed being about seven times higher than the predictions based on the conventional H01then wave function and more 368
than twice as large as the tail prredicted by the Reid soft core wave function (having one of the "thickest" tails) with D wave included. If we make a cut on Ps and plot events with Ps > 350 MeV/c, then three enhancements in Qpn are to be found: at threshold, at about 140 MeV and at 240 MeV, as is shown in fig. 2. The first one at Qpn ~-"0 is akeady known (see e.g. refs. [18,19]) and is usually ascribed to the FSI in the 1 So state of the neutronproton system. Three possible background processes capable of simulating the observed enhancements were considered: (i) Since one might expect some contribution of the single scattering mechanism, the peripheral phase space for proton elementary reaction on bound nucleon was generated by the modified FOWL programme and combined with the spectator nucleon generated according to the following procedure: (a) The spectator nucleon was assumed to be on the mass shell, whereas the mass of the "active" nucleon was calculated from the formula: ma = ([md _ (m 2 + p2)1/212 _ p2~1/2 , where rod, m and Ps are the mass of the deuteron, the nucleon mass and the spectator nucleon momentum generated according to the Reid soft core wave function for Ps > 0.35 GeV/c with D wave contribution taken into account. (b) The momentum of the "active" nucleon was assumed to be opposite to that of
Volume 128B, number 5
PHYSICS LETTERS
1 September 1983
40
35
30
t.t) I--z LI.J
>
25 20
LLI LL 0
J/J
15
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/
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5
",, II
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50
100
150
200
250
300
350
400
450
Op°(MeV) Fig. 2. The excitation energy distribution for the "non-spectator" (ps > 350 MeV/c) sample. The dashed and dotted lines represent the background originated from single and double scattering, respectively. The solid lines refer to the dp ~ pnp three-body phase space alone and together with the two Breit-Wigner distributions.
the spectator one. (c) The angle of emission of the spectator in the deuteron rest system was generated from the isotropic distribution and it was checked for each event whether the generated momentum and the angle of emission are allowed kinematically. (d) The dependence of the slope of four-momentum transfer distribution on the cms energy of the projectile and the moving off shell nucleon from the deuteron was taken into account in the pheripheral phase space calculations [16,20]. The dashed line in fig. 2 shows the result of calculations. The curve is normalized to the half of the events to account for the maximum possible contribution of single scattering. (ii) Likewise we haveexamined the background due to the double scattering effects. The Glauber type calculations [21] yield its maximum contribution of about 3% to all dp -+ (pn)p break-up events, whereas
the sample studied amounts to about 6% of the total number of events. The double scattering background was calculated by using our modified version of FOWL programme and both scatterings were treated in a similar fashion as the first one in the single scattering calculations, with the only difference that in the second collision the nucleon hit by the projectile was already on the mass shell. The Qpn background originated from the double scattering, shown in fig. 2 by dotted line, is quite flat in the interval from 100 to 200 MeV and drops slowly for higher Qpn" Note, that in the impulse approximation and in the double scattering calculations we neglect the FSI in the 3 S1 state [ 16] leading to the formation of deuteron which should certainly reduce the number of events with small Qpn by changing the assignment of the event from one of deuteron break-up back to one of elastic scattering. It is seen from fig. 2 that neither 369
Volume 128B, number 5
PHYSICS LETTERS
the single scattering curve nor the double scattering one nor their sum are able to reproduce the data or be responsible for the observed enhancements. (iii) The three body dp -->pnp phase space was generated and is shown in fig. 2 by solid line. Apart from the Qpn intervals where the enhancements are present, it resembles quite reasonably the shape of the experimental distribution. Leaving aside the threshold enhancement which requires special FSI calculation, we fitted two Breit-Wigner distributions and this background to the data in the Qpn interval from 55 to 275 MeV. The upper cut o f the interval in which the fit was performed is due to some excess of events present in the vicinity o f Qpn ~ 400 MeV. The result of the fit and the background alone are shown in fig. 2 b y solid line. With exception o f the region of the threshold signal, the three-body phase space background and two Breit-Wigner distributions agree fairly well with the data. The small accumulation o f events at about 400 MeV is close to the mass o f the Argonne dibaryon candidate [22] and might be its " p r o t o n neutron" counterpart, but statistics is very limited here. The masses, the widths and the cross sections obtained from the fit are: Q1 = 1 3 5 + 1 0 M e V FI
(M 1 = 2 0 2 0 - + 1 0 M e V ) ,
=45-+20MeV,
o(/1//1) = 200 + 20 p b , Q2 = 2 4 0 + 1 0 M e V
(M 2 = 2 1 3 0 + 1 0 M e V ) ,
F 2 = 20 + l 0 MeV, o(/I//2) = 85 -+ 15 p b , The angular distributions o f nucleons from the (np) excited system in the (np) rest frame with respect to the incoming proton direction were examined for the overall sample in two standard deviation intervals around the masses of the enhancements. The angular distributions exhibit f o r w a r d - b a c k w a r d symmetry, the isotropic component is present in both distributions and the fractions of events distributed isotropicaUy are consistent with the cross sections obtained from the fit for 2020 and 2130 MeV signals. The masses of the observed enhancements fit surprisingly well into the simple scheme developed by MacGregor [23]. He found that the masses o f already
370
1 September 1983
reported 1 D2 ' 3 F3 and 1G 4 [2] dibaryon resonances in the pp system follow a straight line when plotted against I(l + 1). If one assumes, b y analogy to the nuclear physics rotational band, that this is due to the difference in rotational energy, the extrapolation to l = 0 yields a mass o f 2020 MeV, exactly the mass we observe. The second enhancement at 2130 agrees with l = 2 state with the predicted mass o f 2140 MeV. In conclusion we wish to emphasize that there already exist data obtained by working with an incident deuteron beam at higher energies (e.g. at 11.6 [24] and 24 GeV/c [25]) and it would be o f great interest to perform a similar analysis for the "non-spectator" sample. Also the deuterium bubble chamber experiments could yield, with somewhat worse resolution, valuable information about possible dibaryon states.
References [1] A. Yokosawa, ANL report m. ANL-HEP-CP-80-01 (1980), to be published in: Proc. Intern. Meeting on Two-nucleon systems and dibaxyon resonances (Hiroshima, 1979). [2] I.P. Auer et al., Phys. Rev. Lett. 41 (1978) 1436. [ 3] A. Yokosawa, ANL report rtr. ANL-HEP-CP-78-52 (1978). [4] N. Hoshizaki, Prog. Theor. Phys. 60 (1978) 1796. [5] W. Grein and P. KroU, Nucl. Phys. B137 (1978) 173. [6] H. Ikeda et al., Phys. Rev. Lett. 42 (1979) 1321. [7] T. Kamae et al., Phys. Rev. Lett. 38 (1977) 471. [8] T. Siemiarczuk and P. Zielifiski, Phys. Lett. 24B (1967) 675. [9] B. Balcer et al., Acta Phys. Pol. 33 (1968) 619. [10] S. Azimov et al., Yad. Fiz. 19 (1974) 317. [11 ] N. Angelov et al., JINR report P1-80-55 (1980). [12] B.S. Aladashvili et al., Nuel. Phys. A274 (1976) 486. [ 13 ] B.S. Aladashvili et al., J. Phys. (NY) G3 (1977) 1225. [14] B.S. Aladashvili et al., Nucl. Instrum. Methods 129 (1975) 109. [15] R. Harris, Ph.D. Thesis, VTL-PUB-22, University of Washington (1975). [16] B.S. Aladashvili et al., J. Phys. (NY) G3 (1977) 7. [17] G. Alberi et al., Nucl. Phys. B108 (1976) 327. [18] T.R. Witten et al., Nucl. Phys. B108 (1976) 327. [191 T. Ericson, Adv. Phys. 9 (1960) 425. [20] E. Byckling and K. Kajantie, Nuel. Phys. B9 (1969) 568. [21] B.S. Aladashvili et al., Nucl. Phys. B92 (1975) 189. [221 A. Yokosawa, Phys. Rep. 64 (1980) 49. [23] M.H. MacGregor, Phys. Rev. Lett. 42 (1979) 1724. [24] D. Hochman et al., Nucl. Phys. B68 (1974) 301. [25] J.W. Cooper et al., Nucl. Phys. B79 (1974) 259.